Teorema Chinês dos restos e aplicações

Abstract

The focus of this research is the Chinese Remains problem and some of its elementary applications. To achieve this goal, from Chapters 2 to 5, we appoach some content in the bibliographic review, among which we can highlight: Set of Integer Numbers and their Basic Properties, Integer Division, Greatest Common Divisor, Common Multiple Minimum, Linear Diophantine Equations and Congruences. In addition, some content has been dealt with in a deeper way than is usually done in basic education, because although it plays an important role in solving many problems involving whole numbers, they are somewhat underutilized in basic education, especially when these are fundamentals for Olympics and Mathematics graduations. In Chapter 6 we present the proof of the Chinese Remainder Theorem and nine examples of its applications. We believe that such issues, in the way they were handled in this monograph can be supportive for teachers and students seeking supplementary problem solving materials.